#### Answer

$f^{-1}(x) = \frac{5 + 7x}{x - 2}$

#### Work Step by Step

$f(x) = \frac{2x + 5}{x - 7}$
$y = \frac{2x + 5}{x - 7}$
y(x - 7) = 2x + 5
yx - 7y = 2x + 5
yx - 2x = 5 + 7y
x(y - 2) = 5 + 7y
$x = \frac{5 + 7y}{y - 2}$
$f^{-1}(x) = \frac{5 + 7x}{x - 2}$